We　study　a　new　competitive　multi-facility　location　and　quality　design　problem　in　a　continuous　space.　The　facility　location　and　quality　design　are　considered　together　because　of　their　interdependence.　Especially,　new　entrant　facilities　compete　for　customer　demands　with　existing　ones　and　the　latter＇s　reactions　are　taken　into　account.　The　goal　is　to　maximize　the　profit　of　all　new　entrant　facilities　by　optimally　determining　their　locations　and　qualities.　For　this　problem,　a　probabilistic　Huff-like　gravity　model　is　adopted　to　analyze　the　market　share　to　be　captured　by　new　and　existing　facilities,　and　then　a　mathematical　programming　model　is　provided　based　on　the　market　share　analysis.　Since　it　is　shown　to　be　strongly　NP-hard,　a　new　iterative　solution　framework　is　first　proposed　to　solve　it,　where　at　each　iteration,　new　configurations　of　facility　locations　are　firstly　generated,　and　then　the　quality　decisions　of　all　facilities　are　modelled　as　a　competitive　decision　process　by　a　non-cooperative　game.　The　best　qualities　for　new　and　existing　facilities　are　determined　by　their　Nash　equilibrium.　Finally,　optimal　or　near-optimal　solutions　are　calculated.　Then　based　on　the　proposed　solution　framework,　a　particle　swarm　optimization-based　approach　is　developed.　Computational　results　for　randomly　generated　instances　indicate　that　the　devised　algorithm　is　able　to　find　suitable　locations　and　qualities　of　newly　entering　facilities　in　a　competitive　environment　and　outperforms　favorably　a　genetic　algorithm-based　approach.